Conservative-dissipative approximation schemes for a generalized Kramers equation
Analysis of PDEs
2012-06-14 v1 Mathematical Physics
math.MP
Abstract
We propose three new discrete variational schemes that capture the conservative-dissipative structure of a generalized Kramers equation. The first two schemes are single-step minimization schemes while the third one combines a streaming and a minimization step. The cost functionals in the schemes are inspired by the rate functional in the Freidlin-Wentzell theory of large deviations for the underlying stochastic system. We prove that all three schemes converge to the solution of the generalized Kramers equation.
Keywords
Cite
@article{arxiv.1206.2859,
title = {Conservative-dissipative approximation schemes for a generalized Kramers equation},
author = {Manh Hong Duong and Mark A. Peletier and Johannes Zimmer},
journal= {arXiv preprint arXiv:1206.2859},
year = {2012}
}